numerical analysis of regenerative cooling in liquid

Aerospace Science and Technology 24 (2013) 187–197

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Numerical analysis of regenerative cooling in liquid propellant rocket engines

A. Ulas ∗, E. Boysan

Department of Mechanical Engineering, Middle East Technical University, 06800, Ankara, Turkey

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 August 2011Received in revised form 1 November 2011Accepted 4 November 2011Available online 18 November 2011

Keywords:Liquid propellant rocket enginesRegenerative coolingCooling efficiencyCooling channelLiquid oxygenKerosene

High combustion temperatures and long operation durations require the use of cooling techniques inliquid propellant rocket engines (LPRE). For high-pressure and high-thrust rocket engines, regenerativecooling is the most preferred cooling method. Traditionally, approximately square cross sectional coolingchannels have been used. However, recent studies have shown that by increasing the coolant channelheight-to-width aspect ratio and changing the cross sectional area in non-critical regions for heat flux, therocket combustion chamber gas-side wall temperature can be reduced significantly without an increasein the coolant pressure drop. In this study, the regenerative cooling of a liquid propellant rocket enginehas been numerically simulated. The engine has been modeled to operate on a LOX/kerosene mixture ata chamber pressure of 60 bar with 300 kN thrust and kerosene is considered as the coolant. A numericalinvestigation was performed to determine the effect of different aspect ratio and number of coolingchannels on gas-side wall and coolant temperatures and pressure drop in cooling channels.

© 2011 Elsevier Masson SAS. All rights reserved.

1. Introduction

Regenerative cooling is one of the most widely applied coolingtechniques used in LPRE [7]. It has been effective in applicationswith high chamber pressure and for long durations with a heatflux range 1.6 to 160 MW/m2 [12]. In LPRE, the nozzle throat re-gion usually has the highest heat flux and is therefore the mostdifficult region to cool.

Recent studies [2,14,13] have shown that by increasing thecoolant channel height-to-width aspect ratio and changing thecross sectional area in non-critical regions for heat flux, the rocketcombustion chamber wall temperatures can be reduced signifi-cantly without an increase in the coolant pressure drop.

In regenerative cooling process, the coolant, generally the fuel,enters passages at nozzle exit of the thrust chamber, passes bythe throat region and exits near the injector face. The passagesformed either by brazing cooling tubes to the thrust chamber or bymilling channels along the wall of the thrust chamber. The cross-sections of the rectangular passages are smaller in the high heatflux regions to increase the velocity of the coolant. In 1990, by con-ventional manufacturing techniques, aspect ratios (ratio of channelheight to channel width) as high as 8 could be manufacturedand by introducing the platelet technology aspect ratio of cool-ing channels is increased as high as 15 [2]. Today, improvementsin manufacturing technologies have shown that by conventionalmanufacturing methods, cooling channels with an aspect ratio 16(8 mm height and 0.5 mm width) can be milled [8].

* Corresponding author. Tel.: +90 312 210 5260; fax: +90 312 210 2536.E-mail address: [email protected] (A. Ulas).

1270-9638/$ – see front matter © 2011 Elsevier Masson SAS. All rights reserved.doi:10.1016/j.ast.2011.11.006

The heat transfer analysis in regenerative cooling is simplybased on convection and radiation heat transfer for gas domain,conduction heat transfer for solid domain and convection heattransfer for liquid domain. Several different computational fluiddynamics (CFD) computer programs have been used for the anal-ysis of thrust chamber steady-state heat transfer, with differentchamber geometries or different materials with temperature vari-able properties. Rocket thermal evaluation (RTE) code [9] and two-dimensional kinetics (TDK) nozzle performance code [4] are exam-ples for such CFD tools, which are developed for the analysis ofliquid propellant rocket engines with regenerative cooling.

In this study, the effects of geometry (i.e. aspect ratio) andnumber of cooling channels on cooling efficiency are investigatedin terms of the maximum temperature of thrust chamber wall andcoolant, and the pressure drop in cooling channel.

2. Mathematical description and solution method

2.1. Mathematical description

The solution domain used in this study consists of 3 medium:coolant, thrust chamber, and chamber jacket. Because of the sym-metry characteristic of the system, the domain is divided by twosymmetry planes (Fig. 1).

In this study the fluid flow and heat transfer in the coolingchannel was assumed to be three-dimensional, steady-state, andturbulent flow. The conservation equations of fluid flow and heattransfer are expressed as:

∇ · (ρ−→V φ) = ∇ · (Γφ∇φ) + Sφ (1)

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188 A. Ulas, E. Boysan / Aerospace Science and Technology 24 (2013) 187–197

Nomenclature

A Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2

C∗ Characteristic velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/sC1 Constant in turbulence modelC2 Constant in turbulence modelCμ Constant in turbulence modelCp Specific heat at constant pressure . . . . . . . . . . . . . . . J/kg KD Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mDh Hydraulic diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . mH Heat transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . W/m2 Km Mass flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/sn Normal outward directionP Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . barPr Prantl numberq Heat flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W/m2

r Recovery factorM Mach numberT Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ku Velocity along x direction . . . . . . . . . . . . . . . . . . . . . . . . . m/sv Velocity along y direction . . . . . . . . . . . . . . . . . . . . . . . . . m/sω Velocity along z direction . . . . . . . . . . . . . . . . . . . . . . . . . m/s

Other symbols

σκ Turbulent Prandtl numbers for κσε Turbulent Prandtl numbers for εσT Turbulent Prandtl numbers for Tρ Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/m3

γ Specific heat ratioμ Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/m sμeff Effective turbulence viscosity . . . . . . . . . . . . . . . . . . . kg/m sμt Turbulence viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/m s

Subscripts

aw Adiabatic wall temperaturec Chamberconv ConvectionCO2 Carbon dioxideH2O Water vaporg Gas domainpr Propellantrad Radiationt Throatwg Gas side wall

Fig. 1. Schematic view of solution domain.

where the expressions of φ, Γφ and Sφ for different variables aregiven in Table 1.

The effect of heat transfer from hot combustion gases to the so-lution domain is considered in two parts: convection and radiationheat transfers. Convection heat flux can be given as:

qconv = hg(Taw − Twg) (2)

Heat transfer coefficient is calculated using Bartz Correlation [1]as:

hg = 0.026

d0.2t

(μ0.2

c Cp,c

Pr0.6c

)(Pc

C∗

)0.8( At

A

)0.9

σ (3)

σ =[

0.5Twg

Tc

(1 + γ − 1

2M2

)+ 0.5

]−0.68

×(

1 + γ − 1M2

)−0.12

(4)
2
Taw = Tc

[1 + r( γ −1

2 )M2

1 + (γ −1

2 )M2

](5)

where r = (Prc)0.33 for turbulent flows.

For the propellants containing only carbon, hydrogen, oxygen,and nitrogen atoms, the total radiation heat flux, can be approxi-mated as [3]:

qrad ≈ qrad,CO2 + qrad,H2O (6)

qrad,CO2 = 3 3√

pCO2 Le

[(Taw

100

)3.5

−(

Twg

100

)3.5 ](7)

qrad,H2O = 3p0.8H2OL0.6

e

[(Taw

100

)3

−(

Twg

100

)3 ](8)

2.2. Solution method

FLUENT [5], a pressure based segregated solver, is used for thesolution of the governing equations. Standard k–ε two-equation

A. Ulas, E. Boysan / Aerospace Science and Technology 24 (2013) 187–197 189

Table 1Conservation equation variables.

Equations φ Γφ Sφ

Continuity 1 0 0

u u μeff − ∂ p∂x + ∂

∂x

(μeff

∂u∂x

) + ∂∂ y

(μeff

∂v∂x

) + ∂∂z

(μeff

∂ω∂x

)v v μeff − ∂ p

∂ y + ∂∂x

(μeff

∂u∂ y

) + ∂∂ y

(μeff

∂v∂ y

) + ∂∂z

(μeff

∂ω∂z

)ω ω μeff − ∂ p

∂z + ∂∂x

(μeff

∂u∂z

) + ∂∂ y

(μeff

∂v∂z

) + ∂∂x

(μeff

∂ω∂z

)Energy T μ/Pr + μ/σT 0

k k μ + (μ/σk) ρGk − ρε

ε ε μ + (μ/σε)εk (C1ρGk − C2ρε)

Gk = ( μtρ

)[(∂u∂x

)2 + (∂ω∂ y

)2 + (∂ω∂z

)2] + ((∂u∂ y

) + (∂v∂x

))2 + ((∂u∂z

) + (∂ω∂x

))2 + ((∂v∂z

) + (∂ω∂ y

))2

Cμ = 0.09 C1 = 1.44 C2 = 1.92 σk = 1.0 σε = 1.3 σT = 0.85

Fig. 2. Schematic view of solution method.

turbulence model is employed with standard wall functions. SIM-PLE algorithm is used to get the pressure field. NASA computerprogram CEA [10] is used to obtain the thermal properties of thecombustion gas mixture. A User Defined Function (UDF), which iscoupled with the solver, calculates the heat flux from combustedgases to the solution domain in terms of Twg using Eqs. (2) and (6).Thermal properties of combusted gases are given as an input datafrom the CEA code. The UDF gets the coordinates of the nodes fromthe solver to calculate Mach number and area which are used inEq. (3). GAMBIT [6] is used for grid generation. The grid is gener-ated by hexahedral elements in consideration of structured mesh.Solution method used in this study is given in a schematic view inFig. 2.

3. Validation of the solver

Validation of the solution method was performed using the ex-perimental study of Wadel and Meyer [14] and numerical studyof Wadel [13]. They used an 89-kN thrust engine having gaseoushydrogen (GH2) fuel and liquid oxygen (LOX) oxidizer in their ex-perimental studies [14]. The coolant was liquid hydrogen (LH2).The thrust chamber consisted of oxygen free high conductivity(OFHC) copper inner wall with INCONEL-718 outer shell. Chamberliner was milled with 100 conventional coolant channels. Thesechannels had an aspect ratio of 2.5. In the critical heat flux area(nozzle throat region) cooling channels were bifurcated into 200channels and aspect ratio was increased up to 8. For bifurcated

channel cooling systems, channels were split into two channelsand combined back to a single channel. To get the temperaturevalues on the hot-gas-side wall, nine thermocouples were insertedinto holes drilled in the centre of the coolant channel ribs. Alsopressure taps were placed in the locations of coolant channel in-let and outlet. The tests were performed for different mass flowrates in cooling channels. Gas side wall temperature distributionsand pressure drops in the channels were obtained [14].

The numerical solution method [13] was validated with the ex-periments explained above. For numerical analysis, RTE and TDKcodes were used. Radiation effects were not considered in theanalysis. After the validation of numerical method, Wadel per-formed a numerical study for comparison of high aspect ratiocooling channel designs [13]. In this study seven different cool-ing channel designs were compared according to their coolingefficiencies. First design was called as “Baseline” and had 100 con-tinuous cooling channels with an aspect ratio of 2.5 and constantcross-sectional area. Fifth design was the bifurcated model whichcorresponded to the experimental data performed by Wadel andMeyer [14]. For the validation of solution method used in thisstudy these two models are considered.

3.1. Baseline solution

3.1.1. Grid convergenceThe solution domain consist of 3 sub-domains; inner wall, outer

shell and coolant. To obtain grid independent results, solution do-


Table 2Grid specifications.

CASE 01 CASE 02 CASE 03 CASE 04 CASE 05

Grid type (inner wall) Tetrahedral Tetrahedral Tetrahedral Tetrahedral Tetrahedral

# of elements (inner wall) 56,672 56,672 56,672 56,672 56,672

Grid type (outer shell) Tetrahedral Tetrahedral Tetrahedral Tetrahedral Tetrahedral

# of elements (outer shell) 104,026 104,026 104,026 104,026 104,026

Grid type (coolant) Hexahedral Hexahedral Hexahedral Hexahedral Hexahedral

# of elements (coolant) 82,134 167,112 450,400 1,014,000 4,563,000

Thickness of first row (coolant) 10 μm 5 μm 1 μm 0.5 μm 0.1 μm

Total number of elements 211,832 296,810 580,098 1,143,698 4,692,698

Fig. 3. Cross-sectional view of solution domains.

Fig. 4. Convergence history of pressure drop.

main is generated for 5 cases having different number of elementsin the coolant domain. For solid domains tetrahedral elements andfor coolant domain hexahedral elements are used. Between thesub-domains non-conformal grid boundary is used. The specifica-tions of the grid for 5 cases are given in Table 2 and the cross-section of the solution domains are given in Fig. 3.

3.1.2. Baseline solution resultsConvergence histories of temperature rise and pressure drop in

cooling channels with respect to number of elements are obtained.Fig. 4 shows the pressure drop in the channel versus number ofelements. Solution results of the five cases along with the Wadel’ssolution [13] are given in Table 3.

As can be seen from these results, as the number of elementsincreased the solution is converged. The results for CASE 04 andCASE 05 are quite similar and at this point the grid specificationsfor CASE 04 are enough to get grid independent solutions. There-fore for the following analysis in this study, grids will be generatedaccording to the grid specifications of CASE 04.

3.2. Bifurcation channel solution results

By using the grid specifications of CASE 04, the solution do-main is generated for bifurcation channel. Results are obtainedby present solution method and compared with the numerical


Table 3Results of baseline solution.

Tmax on gasside wall [K]

Pressure drop inchannel �P [bar]

Temperature risein channel �T [K]

CASE 01 882.7 53.8 216.8CASE 02 816.9 51.4 229.8CASE 03 783.2 45.7 265.4CASE 04 755.07 40.5 297.8CASE 05 748.4 40.1 302.8Wadel’s

solution [13]764 37 –

Table 4Comparison of pressure values for bifurcation channel solution.

P inlet [bar] Poutlet [bar] �P [bar]

Present numericalsolution

175.0 138.3 36.7

Wadel’s numericalsolution [13]

175.0 135.5 40.0

Wadel and Mayer’sexperimental data [14]

175.0 125.0 50.0

and experimental solutions of Wadel and Meyer in Table 4 andFig. 5.

The numerical results from this study are quite similar withthe numerical [13] and experimental results found in literature[14]. Although there are some differences between temperatureand pressure values, these differences are acceptable. The reasonsfor the differences could be the uncertainties on cooling chan-nel geometry, which are given roughly in the literature [14,13],and differences in material thermal properties used in the solu-tions.

In this study, the main aim is to see the effect of different as-pect ratio and number of cooling channels on cooling efficiency,therefore, the present solution method is considered to be suit-able and sufficient to understand the effect of these parameters oncooling efficiency.

Table 5LPRE specifications.

Thrust [kN] 300Combustion chamber pressure [bar] 60Exit pressure [bar] 1.5Ambient pressure [bar] 1Fuel Kerosene (RP-1)Oxidizer LOXOxidizer-to-fuel ratio 7:3Theoretical specific impulse at sea level [s] 295Adiabatic Falme temperature [K] 3570Oxidizer mass flow rate [kg/s] 72.7Fuel mass flow rate [kg/s] 31.1Nozzle expansion area ratio 6.573Throat diameter [mm] 200Nozzle exit diameter [mm] 512Chamber dameter [mm] 306

4. Results and discussions

Numerical analyses are performed in this study for a thrustchamber with specifications given in Table 5. NCDT (Nozzle Con-tour Design Tool) code [11] is used to estimate the nozzle contourfor diverging part.

Materials used in the analysis are defined as kerosene (RP-1)for the coolant, OFHC copper for the inner wall and INCONEL-718for the outer shell. Surface roughness for metal structures is takenas 3.5 μm.

4.1. Boundary conditions

Boundary conditions for solution domain (Fig. 6) are given inTables 6, 7, and 8.

4.2. Effect of radiation heat transfer

To examine the radiation heat transfer effect, two analyses areperformed with the same cooling channel geometry under differ-ent heat flux boundary conditions. Analysis parameters are givenin Table 9.

Fig. 5. Temperature distributions on gas-side wall for bifurcation channel solution.


Fig. 6. Designations of the boundaries of solution domain.

Table 6Boundary conditions for inner wall.

Plane ABGFDC ∂T∂n = 0

Plane JKPOML ∂T∂n = 0

Plane BGPK ∂T∂n = 0

Plane ACLJ ∂T∂n = 0

Plane ABKJ ∂(kT )∂n = qg

Table 7Boundary conditions for outer shell.

Plane EFGIH ∂T∂n = 0

Plane NOPRS ∂T∂n = 0

Plane EHRN ∂T∂n = 0

Plane GISP ∂T∂n = 0

Plane HIRS ∂T∂n = 0

Table 8Boundary conditions for coolant.

Plane LMONa m = mpr2×N , T = T inlet

Plane CDFEb P = Pc

Plane CENL ∂u∂n = ∂v

∂n = ∂ w∂n = ∂T

∂n = 0

a N refers to number of cooling channels. T inlet is the initial tem-perature of coolant and 300 K for all analyses.

b Pressure loses in injector are neglected. Therefore coolant exitpressure should be at combustion chamber pressure in ideal condi-tions. For all analyses exit pressure of coolant is 60 bar.

Table 9Parameters for radiation heat transfer investigation.

4 × 4 × 100(no radiation)

4 × 4 × 100

Channel height [mm] 4 4Channel width [mm] 4 4# of cooling channels 100 100Heat flux (qg) Convection Convection, radiationCoolant mass flow rate

(per channel) [kg/s]0.311 0.311

Table 10Results for radiation heat transfer investigation.

4 × 4 × 100(no radiation)

4 × 4 × 100

Maximum heat flux on gasside wall [MW/m2]

28.43 29.32

Maximum wall temperatureon gas side [K]

783.7 801.8

Maximum coolanttemperature [K]

647.1 669.8

Required pressure inlet forcoolant [bar]

78.1 77.8

Pressure drop in channel [bar] 18.1 17.8

Numerical results are given in Table 10. Radiation heat transferincreases the maximum temperature on the gas side wall by onlyabout 2%, which is quite small; therefore, one could ignore theradiation heat transfer in the numerical analysis. However, in ourfollowing analyses, the sum of radiation and convection heat fluxis still used as a boundary condition for gas side thrust chamberwall.


Table 11Parameters for 4 mm height channels.

4 × 5 × 100 4 × 4 × 100 4 × 3 × 100 4 × 2 × 100 4 × 1 × 100

Channel height [mm] 4 4 4 4 4Channel width [mm] 5 4 3 2 1# of cooling channels 100 100 100 100 100AR (aspect ratio) 0.8 1.0 1.3 2.0 4Dh [mm] 4.4 4.0 3.4 2.7 1.6Heat flux (qg) Convection Convection Convection Convection Convection

Radiation Radiation Radiation Radiation Radiationm (per channel) [kg/s] 0.311 0.311 0.311 0.311 0.311Channel geometry

Table 12Parameters for 8 mm height channels.

8 × 5 × 100 8 × 4 × 100 8 × 3 × 100 8 × 2 × 100 8 × 1 × 100

Channel height [mm] 8 8 8 8 8Channel width [mm] 5 4 3 2 1# of cooling channels 100 100 100 100 100AR (aspect ratio) 1.6 2.0 2.7 4.0 8.0Dh [mm] 6.2 5.3 4.4 3.2 1.8Heat flux (qg) Convection Convection Convection Convection Convection

Radiation Radiation Radiation Radiation Radiationm (per channel) [kg/s] 0.1555 0.1555 0.1555 0.1555 0.1555Channel geometry

Table 13Results for 4 mm height channels.

4 × 5 × 100 4 × 4 × 100 4 × 3 × 100 4 × 2 × 100 4 × 1 × 100

Maximum heat flux ongas side wall [MW/m2]

29.03 29.32 29.53 29.67 29.74


822.3 801.8 787.5 777.9 773.2


681.2 669.8 659.2 649.7 640.3

Required pressure inletfor coolant [bar]

70.3 77.8 96.3 164.0 741.0

Pressure drop inchannel [bar]

10.3 17.8 26.3 104.0 681.0

Table 14Results for 8 mm height channels.

8 × 5 × 100 8 × 4 × 100 8 × 3 × 100 8 × 2 × 100 8 × 1 × 100


27.33 27.90 28.36 28.79 29.24


944.5 904.9 872.5 842.7 811.8


805.0 760.6 724.0 703.4 679.0


61.9 63.4 67.6 83.3 247.2

Pressure drop inchannel [bar]

1.9 3.4 7.6 23.3 187.2

4.3. Effect of channel geometry on cooling efficiency

The effect of channel geometry on cooling efficiency is ex-amined in two groups. In each group the height of the coolingchannels are constant and width of the channels are decreasedgradually. For the first group height is 4 mm and for the second

group height is 8 mm. Analysis parameters are given in Tables 11and 12. The results are given in Tables 13 and 14.

These results show that for the same mass flow rate (i.e., samenumber of cooling channels) and channel height, gas-side wall andcoolant temperatures decrease with the increase of the aspect ra-tio. This is because as we decrease the width of the cooling chan-


Fig. 7. Velocity profiles of coolant at throat (x = 0).

Fig. 8. Effects of aspect ratio on gas side wall temperature.

nels (i.e., increasing aspect ratio), velocity, Reynolds number, andtherefore heat transfer coefficient on coolant side wall increases.The increase of the flow velocity in the cooling channels with theincrease of the aspect ratio can be observed in Fig. 7, which showscoolant velocity profiles in the channel at the throat (x = 0) foreach geometry.

With constant channel height and channel number, the cool-ing efficiency has a converging trend, as shown in Fig. 8, due tothe opposing effect between the decrease of heat transfer area

and increase of heat transfer coefficient, as the aspect ratio in-creases. The decrease of the wall temperature is good from thestructural design point of view; however, as one can see from Ta-bles 13 and 14, the pressure drop in the channels reaches verylarge values, as high as 681 bar, for larger aspect ratios. For chan-nel geometries 4 × 2 × 100, 4 × 1 × 100, and 8 × 1 × 100, pressuredrops are calculated as higher than the combustion chamber pres-sure (60 bar) and therefore these designs are not acceptable sincethey need large feeding systems. Pressure drops around half of the


Table 15Parameters used in the analysis for the effect of number of channels on cooling efficiency.

4 × 2 × 50 4 × 2 × 100 4 × 2 × 150 4 × 2 × 200 4 × 2 × 250 4 × 2 × 300

Channel height [mm] 4 4 4 4 4 4Channel width [mm] 2 2 2 2 2 2# of cooling channels 50 100 150 200 250 300AR (aspect ratio) 2.0 2.0 2.0 2.0 2.0 2.0Dh [mm] 2.7 2.7 2.7 2.7 2.7 2.7Heat flux (qg) Convection Convection Convection Convection Convection Convection

Radiation Radiation Radiation Radiation Radiation Radiationm (per channel) [kg/s] 0.6220 0.3110 0.2073 0.1555 0.1244 0.1037

Table 16Results obtained from the analysis for the effect of number of channels on cooling efficiency.

4 × 2 × 50 4 × 2 × 100 4 × 2 × 150 4 × 2 × 200 4 × 2 × 250 4 × 2 × 300

Maximum heat flux on gasside wall [MW/m2]

29.07 29.67 29.83 29.71 29.39 28.67


821.7 777.9 770.5 778.6 800.6 850.1


654.8 649.7 647.3 649.3 654.4 695.5

Required pressure inlet forcoolant [bar]

411.9 164.0 110.8 90.3 80.3 74.6

Pressure drop in channel[bar]

351.9 104.0 50.8 30.3 20.3 14.6

Fig. 9. Effects of number of channels on gas side wall temperature.

combustion chamber pressure can be used as a system design cri-teria.

4.4. Effect of number of channels on cooling efficiency

According to the analysis results obtained in Section 4.3, coolantchannels with 4 × 1 and 4 × 2 mm2 cross-sectional areas have thebest temperature results for cooling but have high pressure drops(681 bar and 104 bar, respectively). Although these two geome-tries are not suitable because of high pressure drops, by changingthe number of coolant channels, it is possible to decrease pres-sure drops and wall temperatures. Since the wall temperatures arequite close for these geometries, there is no need to work on casewith 4 × 1 mm2 area, which has a very high pressure drop. There-fore, the channel geometry with 4 × 2 mm2 cross-sectional area isselected to investigate the effect of number of channels on coolingefficiency.

The effect of number of channels on cooling efficiency is inves-tigated for 6 different channel numbers. Analysis parameters aregiven in Table 15.

The results are given in Table 16. For small number of coolantchannels, mass flow rate of the coolant and therefore coolant ve-locities are high in each channel. Maximum coolant side heattransfer coefficient is obtained for geometry with 50 channels buton the other hand this geometry has also the minimum total heattransfer area between the coolant and the wall, which results inhigher wall temperatures. As we increase the number of channels,total heat transfer area increases and wall temperatures decrease.These results show that there exists an optimum number of cool-ing channels which has the highest heat flux and lowest tempera-ture on gas side wall, which can be also observed from Fig. 9. For4 × 2 mm2 cross-sectional area, optimum number of cooling chan-nels is around 150.

Pressure drops in the cooling channels also decrease with in-creasing the number of channels due to lower flow velocities. From


Fig. 10. Variation of the cooling channel geometry along the axial direction.

Table 16, one can see that there is more than 50% reduction inthe pressure drop (104 bar versus 50.8 bar) when the number ofcooling channels increase from 100 to 150. Although this is a sig-nificant decrease, 50.8 bar pressure drop is still very high. Anotherway to decrease this pressure drop further is to use cooling chan-nels with variable cross-sectional area, which is discussed in thenext section.

4.5. Cooling channels with variable cross-sectional area (VCSA)

To understand the effects of VCSA on temperature and pres-sure, new cooling channel geometry is formed. The channel has4×2 mm2 cross-sectional area in the throat region and 4×4 mm2

cross-sectional areas in the combustion region and nozzle diverg-ing region. The variation of the cooling channel geometry along therocket engine axis is shown in Fig. 10.

To make a comparison with the results for 4 × 2 × 150 channelgeometry, the number of cooling channels is kept 150 in this anal-ysis. From the results presented in Table 17, we see that there is avery small difference between the maximum heat flux and maxi-mum wall temperature on gas side for 4 × 2 × 150 and VCSA×150cases. However, the major advantage of using VCSA cooling chan-nels can be observed by comparing the pressure drops in the chan-nels. For 4 × 2 × 150 case the pressure drop is 50.8 bar, whereas,

Table 17Results for VCSA×150 and 4 × 2 × 150.

4 × 2 × 150 VCSA×150


29.83 29.82


770.5 772.2


647.3 675.2


110.8 78.4

Pressure drop in channel[bar]

50.8 18.4

for VCSA×150 case the pressure drop is significantly reduced to18.4 bar, which means a more than 60% reduction.

As can be seen from Fig. 11, velocities are high in the throatregion and low in the combustion and nozzle diverging regions.Therefore a better cooling efficiency in the throat region is ob-tained compared to combustion and nozzle diverging regions.Since for both 4 × 2 × 150 and VCSA×150 cases the cross-sectionalarea is the same in the throat region, temperature values are quitesimilar in this region, as shown in Fig. 12. But as we increased thecross-sectional area in combustion and nozzle diverging regions,the cooling efficiency decreases and the wall and coolant tempera-tures of VCSA×150 case become higher than those of 4 × 2 × 150case (Fig. 12).

In Fig. 13, the pressure distributions along the axial directionfor 4 × 2 × 150 and VCSA×150 channel geometries are given. ForVCSA geometry the slope of pressure curve is low for larger cross-section regions and the slope of pressure curve is high for smallercross-section region.

When we analyzed all the results obtained so far, the bestselection for the cooling channels would be the VCSA×150. ForVCSA×150, the maximum wall temperature on the gas side is cal-culated as 772.2 K. For OFHC copper, the melting temperature is1356 K. Therefore we can conclude that no melting of thrust cham-ber material will be observed. The maximum coolant temperatureis calculated as 675.2 K. In Ref. [12], the critical temperature andcritical pressure of kerosene is given as 678 K and 20 bar. The pres-sure levels in the cooling channels are above this critical pressurefor VCSA×150 case, therefore, no boiling occurs in the coolant [7].Pressure drop in the cooling channels for VCSA×150 case is cal-culated as 18.4 bar which is acceptable for a regeneratively cooledrocket engine with 60 bar chamber pressure.

Fig. 11. Velocity profiles of coolant for VCSA channel at different axial locations.


Fig. 12. Temperature distributions along axial direction for 4 × 2 × 150 and VCSA×150 channel geometries: (a) gas side wall temperatures, (b) coolant temperatures.

Fig. 13. Pressure distribution of coolant along axial direction for 4 × 2 × 150 andVCSA×150 channel geometries.

5. Conclusions

In this study, the effects of geometry and number of coolingchannels on the maximum temperatures of thrust chamber walland coolant, and the pressure drop in cooling channel of a liquidpropellant rocket engine are investigated.

Sixteen different design cases, with different geometry andnumber of cooling channels, are investigated. Among these cases,the VCSA channel geometry having 150 cooling channels gives thebest results from the engineering point of view.

Based upon the results of this study, the following conclusionscan be made:

• Increasing the aspect ratio with constant number of coolingchannels will increase the cooling efficiency up to an optimumlevel, and then efficiency will decrease because of decreasingheat transfer area.

• Increasing the aspect ratio with constant number of coolingchannels will increase the pressure drop in cooling channels.

• Increasing the number of cooling channels without changingthe geometry will increase the cooling efficiency up to an op-timum level due to the dominating effect of increasing totalheat transfer area, and then efficiency will decrease because ofthe dominating effect of decreasing mass flow rate per chan-nel.

• Increasing the number of cooling channels without changingthe geometry will decrease the pressure drop in channels.

• Increasing the cross-sectional area of a channel in non-criticalregions of the cooling channel will slightly decrease the cool-ing efficiency and increase the local temperatures, however,the pressure drop decreases significantly.

References

[1] D.R. Bartz, A simple equation for rapid estimation of rocket nozzle convec-tive heat transfer coefficients, Technical notes, DA-04-495, California Instituteof Technology, 1957.

[2] J. Carlie, R. Quentmeyer, An experimental investigation of high-aspect-ratiocooling passages, in: AIAA/SAE/ASME/ASEE 28th Joint Propulsion Conference,Nashville, TN, July 6–8, 1992, AIAA Paper No. 92-3154.

[3] G.D. Ciniaref, M.B. Dorovoliski, Theory of Liquid-Propellant Rockets, Moscow,1957.

[4] S.S. Dunn, D.E. Coats, J.C. French, TDK’02™ Two-Dimensional Kinetics (TDK)Nozzle Performance Computer Program, User’s Manual, Software & Engineer-ing Associates, Inc., 2002.

[5] FLUENT®, http://www.fluent.com/software/fluent/index.htm.[6] GAMBIT®, http://www.fluent.com/software/gambit/index.htm.[7] D.K. Huzel, D.H. Huang, Modern Engineering for Design of Liquid-Propellant

Rocket Engines, AIAA, Washington, DC, 1992.[8] Mitsubishi Materials, C003E General Catalogue, 2007–2009.[9] M.H.N. Naraghi, RTE—A Computer Code for Three-Dimensional Rocket Thermal

Evaluation, User Manual, Tara Technologies, LLC, Yorktown Heights, NY, 2002.[10] G.J. Sanford, M. Bonnie, Computer program for calculation of complex chemi-

cal equilibrium compositions and applications, NASA RP-1311, Washington, DC,1994.

[11] B. Seçkin, Rocket nozzle design and optimization, Dissertation, Middle EastTechnical University, 2003.

[12] G.P. Sutton, Rocket Propulsion Elements, 6th edn., John Wiley & Sons, Inc., NewYork, 1992.

[13] M.F. Wadel, Comparison of high aspect ratio cooling channel designs fora rocket combustion chamber with development of an optimized design,NASA/TM-1998-206313, Washington, DC, 1998.

[14] M.F. Wadel, M.L. Meyer, Validation of high aspect ratio cooling in an 89-kNthrust chamber, in: AIAA/SAE/ASME/ASEE 32nd Joint Propulsion Conference,Lake Buena Vista, Florida, July 1–3, 1996, AIAA Paper No. 96-2584.

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numerical analysis of regenerative cooling in liquid

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